[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.21,0:00:02.13,Default,,0000,0000,0000,,- [Presenter] So we have\Nthis pretty complicated,
Dialogue: 0,0:00:02.13,0:00:04.68,Default,,0000,0000,0000,,some would say hairy,\Nexpression right over here.
Dialogue: 0,0:00:04.68,0:00:06.69,Default,,0000,0000,0000,,And what I want you to\Ndo is pause this video
Dialogue: 0,0:00:06.69,0:00:08.43,Default,,0000,0000,0000,,and see if you can simplify this
Dialogue: 0,0:00:08.43,0:00:10.89,Default,,0000,0000,0000,,based on what you know\Nabout exponent rules.
Dialogue: 0,0:00:11.79,0:00:13.74,Default,,0000,0000,0000,,All right, now let's do this together.
Dialogue: 0,0:00:13.74,0:00:15.99,Default,,0000,0000,0000,,There's many ways you could approach this,
Dialogue: 0,0:00:15.99,0:00:18.12,Default,,0000,0000,0000,,but what my brain wants to do is first
Dialogue: 0,0:00:18.12,0:00:21.48,Default,,0000,0000,0000,,try to simplify this part right over here.
Dialogue: 0,0:00:21.48,0:00:26.48,Default,,0000,0000,0000,,I have a bunch of stuff in\Nhere to an exponent power.
Dialogue: 0,0:00:27.03,0:00:30.15,Default,,0000,0000,0000,,And one way to think about\Nthat, if I have, let's say,
Dialogue: 0,0:00:30.15,0:00:32.79,Default,,0000,0000,0000,,A times B
Dialogue: 0,0:00:32.79,0:00:35.70,Default,,0000,0000,0000,,to the, let's call it C, power.
Dialogue: 0,0:00:35.70,0:00:40.29,Default,,0000,0000,0000,,This is the same thing\Nas A to the C times B
Dialogue: 0,0:00:40.29,0:00:41.67,Default,,0000,0000,0000,,to the C power.
Dialogue: 0,0:00:41.67,0:00:44.37,Default,,0000,0000,0000,,So we could do that with\Nthis part right over here.
Dialogue: 0,0:00:44.37,0:00:46.08,Default,,0000,0000,0000,,And actually, let me just simplify this
Dialogue: 0,0:00:46.08,0:00:48.06,Default,,0000,0000,0000,,so I don't have to keep rewriting things.
Dialogue: 0,0:00:48.06,0:00:51.42,Default,,0000,0000,0000,,So this can be rewritten as
Dialogue: 0,0:00:51.42,0:00:54.42,Default,,0000,0000,0000,,5M, or let me be careful.
Dialogue: 0,0:00:54.42,0:00:56.58,Default,,0000,0000,0000,,This is gonna be five squared
Dialogue: 0,0:00:56.58,0:01:01.13,Default,,0000,0000,0000,,times M to the negative one third squared
Dialogue: 0,0:01:02.88,0:01:05.37,Default,,0000,0000,0000,,times N squared,
Dialogue: 0,0:01:05.37,0:01:09.06,Default,,0000,0000,0000,,which is the same thing as 25.
Dialogue: 0,0:01:09.06,0:01:10.71,Default,,0000,0000,0000,,Now if I raise something to an exponent
Dialogue: 0,0:01:10.71,0:01:12.48,Default,,0000,0000,0000,,and then raise that to an exponent,
Dialogue: 0,0:01:12.48,0:01:14.07,Default,,0000,0000,0000,,so there's another exponent property here.
Dialogue: 0,0:01:14.07,0:01:18.06,Default,,0000,0000,0000,,If I have A to the B, and\Nthen I raise that to the C,
Dialogue: 0,0:01:18.06,0:01:19.38,Default,,0000,0000,0000,,then I multiplied the exponents.
Dialogue: 0,0:01:19.38,0:01:24.15,Default,,0000,0000,0000,,This is equal to A to the B times C power.
Dialogue: 0,0:01:24.15,0:01:26.28,Default,,0000,0000,0000,,So here we would multiply these exponents.
Dialogue: 0,0:01:26.28,0:01:28.23,Default,,0000,0000,0000,,So it's 25M.
Dialogue: 0,0:01:28.23,0:01:31.89,Default,,0000,0000,0000,,Two times negative one third\Nis negative two thirds.
Dialogue: 0,0:01:31.89,0:01:35.46,Default,,0000,0000,0000,,And then of course we have\Nthis N squared right over here.
Dialogue: 0,0:01:35.46,0:01:37.11,Default,,0000,0000,0000,,So actually lemme just rewrite everything
Dialogue: 0,0:01:37.11,0:01:38.55,Default,,0000,0000,0000,,so we don't lose too much track.
Dialogue: 0,0:01:38.55,0:01:40.02,Default,,0000,0000,0000,,So we have 75.
Dialogue: 0,0:01:42.30,0:01:43.71,Default,,0000,0000,0000,,I wrote M. 75.
Dialogue: 0,0:01:43.71,0:01:48.03,Default,,0000,0000,0000,,M to the one third. N\Nto the negative seven.
Dialogue: 0,0:01:48.03,0:01:50.58,Default,,0000,0000,0000,,And then I simplified the bottom part.
Dialogue: 0,0:01:50.58,0:01:54.84,Default,,0000,0000,0000,,I'll do that same color. As 25.
Dialogue: 0,0:01:54.84,0:01:58.57,Default,,0000,0000,0000,,M to the negative two thirds
Dialogue: 0,0:01:58.57,0:02:00.75,Default,,0000,0000,0000,,N squared.
Dialogue: 0,0:02:00.75,0:02:02.28,Default,,0000,0000,0000,,Now, some of y'all might\Nimmediately be able
Dialogue: 0,0:02:02.28,0:02:03.84,Default,,0000,0000,0000,,to skip some steps here, but I'll try
Dialogue: 0,0:02:03.84,0:02:05.82,Default,,0000,0000,0000,,to make it very, very explicit.
Dialogue: 0,0:02:05.82,0:02:08.01,Default,,0000,0000,0000,,What I'm going to read, what I'm gonna do
Dialogue: 0,0:02:08.01,0:02:12.45,Default,,0000,0000,0000,,is rewrite this expression\Nas the product of fractions
Dialogue: 0,0:02:12.45,0:02:14.16,Default,,0000,0000,0000,,or as a product of rational expression.
Dialogue: 0,0:02:14.16,0:02:15.39,Default,,0000,0000,0000,,So I could rewrite this.
Dialogue: 0,0:02:15.39,0:02:17.67,Default,,0000,0000,0000,,This is being equal to
Dialogue: 0,0:02:17.67,0:02:20.31,Default,,0000,0000,0000,,75 divided by 25,
Dialogue: 0,0:02:20.31,0:02:21.78,Default,,0000,0000,0000,,which I think you know what that is.
Dialogue: 0,0:02:21.78,0:02:23.55,Default,,0000,0000,0000,,But I'll just write it like that.
Dialogue: 0,0:02:23.55,0:02:28.55,Default,,0000,0000,0000,,Times, and then we'll worry\Nabout these right over here.
Dialogue: 0,0:02:28.68,0:02:31.32,Default,,0000,0000,0000,,Times M to the one third
Dialogue: 0,0:02:31.32,0:02:34.74,Default,,0000,0000,0000,,over M to the negative two thirds,
Dialogue: 0,0:02:34.74,0:02:37.56,Default,,0000,0000,0000,,and then times, I'll put this in blue.
Dialogue: 0,0:02:39.09,0:02:42.54,Default,,0000,0000,0000,,Times N to the negative seven
Dialogue: 0,0:02:42.54,0:02:44.97,Default,,0000,0000,0000,,over N squared.
Dialogue: 0,0:02:44.97,0:02:48.79,Default,,0000,0000,0000,,Now 75 over 25, we know what that is,
Dialogue: 0,0:02:48.79,0:02:49.74,Default,,0000,0000,0000,,that's going to be equal to three.
Dialogue: 0,0:02:49.74,0:02:52.17,Default,,0000,0000,0000,,But how do we simplify\Nthis right over here?
Dialogue: 0,0:02:52.17,0:02:54.06,Default,,0000,0000,0000,,Well, here we can remind ourselves
Dialogue: 0,0:02:54.06,0:02:55.74,Default,,0000,0000,0000,,another exponent property.
Dialogue: 0,0:02:56.85,0:03:01.14,Default,,0000,0000,0000,,If I have, let's call it A to the B
Dialogue: 0,0:03:01.14,0:03:05.34,Default,,0000,0000,0000,,over C to the D, actually it\Nhas to have the same base.
Dialogue: 0,0:03:05.34,0:03:07.62,Default,,0000,0000,0000,,Over A to the C.
Dialogue: 0,0:03:07.62,0:03:08.97,Default,,0000,0000,0000,,This is going to be the same thing
Dialogue: 0,0:03:08.97,0:03:13.08,Default,,0000,0000,0000,,as A to the B minus C power.
Dialogue: 0,0:03:13.92,0:03:16.98,Default,,0000,0000,0000,,So I can rewrite all of this business.
Dialogue: 0,0:03:16.98,0:03:19.47,Default,,0000,0000,0000,,I have my three here.
Dialogue: 0,0:03:19.47,0:03:22.53,Default,,0000,0000,0000,,Three times
Dialogue: 0,0:03:22.53,0:03:24.30,Default,,0000,0000,0000,,M to the one third.
Dialogue: 0,0:03:25.26,0:03:27.39,Default,,0000,0000,0000,,And then I'm gonna subtract this exponent.
Dialogue: 0,0:03:27.39,0:03:29.49,Default,,0000,0000,0000,,We have to be very careful.\NWe're subtracting a negative.
Dialogue: 0,0:03:29.49,0:03:32.97,Default,,0000,0000,0000,,So we're subtracting negative two thirds.
Dialogue: 0,0:03:32.97,0:03:35.61,Default,,0000,0000,0000,,That's all that exponent for M.
Dialogue: 0,0:03:35.61,0:03:38.61,Default,,0000,0000,0000,,And then we're going to have times N
Dialogue: 0,0:03:38.61,0:03:40.81,Default,,0000,0000,0000,,to the negative seven power
Dialogue: 0,0:03:42.28,0:03:43.92,Default,,0000,0000,0000,,minus two.
Dialogue: 0,0:03:43.92,0:03:46.35,Default,,0000,0000,0000,,And so now we are in the home stretch.
Dialogue: 0,0:03:46.35,0:03:48.84,Default,,0000,0000,0000,,This is going to be equal to
Dialogue: 0,0:03:48.84,0:03:52.65,Default,,0000,0000,0000,,three times M to the,
Dialogue: 0,0:03:52.65,0:03:55.74,Default,,0000,0000,0000,,what's one third minus\Nnegative two thirds?
Dialogue: 0,0:03:55.74,0:03:59.34,Default,,0000,0000,0000,,Well, that's the same thing\Nas one third plus two thirds,
Dialogue: 0,0:03:59.34,0:04:02.37,Default,,0000,0000,0000,,which is just three\Nthirds, which is just one.
Dialogue: 0,0:04:02.37,0:04:04.35,Default,,0000,0000,0000,,So this is just M to the first power,
Dialogue: 0,0:04:04.35,0:04:06.21,Default,,0000,0000,0000,,which is the same thing as just M.
Dialogue: 0,0:04:07.22,0:04:09.09,Default,,0000,0000,0000,,And then that is going to be times
Dialogue: 0,0:04:09.09,0:04:12.48,Default,,0000,0000,0000,,negative seven minus two,\Nthat is negative nine.
Dialogue: 0,0:04:12.48,0:04:17.28,Default,,0000,0000,0000,,So times N to the negative\Nninth power. And we are done.
Dialogue: 0,0:04:17.28,0:04:20.52,Default,,0000,0000,0000,,And that is strangely\Nsatisfying to take something
Dialogue: 0,0:04:20.52,0:04:25.14,Default,,0000,0000,0000,,that hairy and make it,\NI guess, less hairy?
Dialogue: 0,0:04:25.14,0:04:26.64,Default,,0000,0000,0000,,Now, some folks might not like
Dialogue: 0,0:04:26.64,0:04:28.47,Default,,0000,0000,0000,,having a negative nine exponent here.
Dialogue: 0,0:04:28.47,0:04:30.15,Default,,0000,0000,0000,,They might want only positive exponents.
Dialogue: 0,0:04:30.15,0:04:32.88,Default,,0000,0000,0000,,So you could actually rewrite\Nthis and we could debate
Dialogue: 0,0:04:32.88,0:04:35.52,Default,,0000,0000,0000,,whether it's actually\Nsimpler or less simple.
Dialogue: 0,0:04:35.52,0:04:38.49,Default,,0000,0000,0000,,But we also know the exponent properties
Dialogue: 0,0:04:38.49,0:04:41.85,Default,,0000,0000,0000,,that if I have A to the negative N,
Dialogue: 0,0:04:41.85,0:04:44.97,Default,,0000,0000,0000,,that is the same thing\Nas one over A to the N.
Dialogue: 0,0:04:44.97,0:04:48.96,Default,,0000,0000,0000,,So based on that, I could\Nalso rewrite this as three.
Dialogue: 0,0:04:50.10,0:04:51.33,Default,,0000,0000,0000,,We do the same color as that three.
Dialogue: 0,0:04:51.33,0:04:55.38,Default,,0000,0000,0000,,As three times M.
Dialogue: 0,0:04:55.38,0:04:57.84,Default,,0000,0000,0000,,And then instead of saying\Ntimes N to the negative nine,
Dialogue: 0,0:04:57.84,0:04:59.55,Default,,0000,0000,0000,,we could say that is over,
Dialogue: 0,0:05:00.91,0:05:03.96,Default,,0000,0000,0000,,that is over, N to the ninth.
Dialogue: 0,0:05:03.96,0:05:07.56,Default,,0000,0000,0000,,So that's another way to\Nrewrite that expression.